Models of Pavlovian Responding: Theory 375Rescorla’s contingency (1968) model is elegant in its sim-
plicity (e.g., contingency effects are explained as increases in
trial types 2 and 3), but suffers from several problems. Unlike
most associative models, it cannot account for (a) the power-
ful effects of trial order (e.g., recency effects) because it
ignores the order in which trials occur; or (b) cue competition
effects (e.g., blocking) because it addresses only single cue
situations. For these reasons, Rescorla abandoned his contin-
gency model in favor of the Rescorla-Wagner (1972) model.
However, other researchers have addressed these deficits by
proposing variants of Rescorla’s contingency model. For ex-
ample, Cheng and Novick (1992) developed a contingency
model that, rather than incorporating all trials, includes selec-
tion rules for which trials contribute to the frequencies used
to compute the conditional probabilities. Their focal set
model succeeds in accounting for cue competition. Addition-
ally, if trials are differentially weighted as a function of
recency, contingency models are able to address trial-order
effects (e.g., Maldonado, Cátena, Cándido, & García, 1999).
Finally, although simple contingency models cannot explain
cue-outcome contiguity effects, this problem is shared with
most models (acquisition- as well as expression-focused) that
decompose experience into discrete trials.
Comparator Models
Comparator models are similar to contingency models in
emphasizing a comparison at the time of testing between the
likelihood of the outcome in the presence and absence of the
cue. However, these models are not based on computation of
event frequencies. Currently, there are two types of com-
parator models. One focuses exclusively on comparisons of
temporal relationships (e.g., rates of outcome occurrence),
whereas the other assumes that comparisons occur on many
dimensions, with time as only one of them.
The best-known timing model of acquired behavior is
Gibbon and Balsam’s (1981; also see Balsam, 1984)scalar-
expectancy theory(SET). According to SET, conditioned re-
sponding is directly related to the average interval between
outcomes during training (i.e., an inverse measure of the pre-
diction of the outcome based on the context), and inversely re-
lated to the interval between cue onset and the outcome (i.e., a
measure of the prediction of the outcome based on the cue.
See chapter by Capaldi in this volume for models of how tem-
poral information might be represented cognitively; here, our
concern is the use of temporal information in modulating be-
havior). Like all timing models (in contrast to the other
expression-focused models), SET is highly successful in ex-
plaining cue-outcome contiguity effects and also does well in
predicting the effects of contingency degradation that occur
when the outcome is presented in the absence of the cue. Al-
though the model accounts for the CS-preexposure effect if
context exposure is held constant, it fails to explain extinction,
because latencies to the outcome are assumed to be updated
only when an outcome occurs. Scalar-expectancy theory also
fails to account for stimulus competition-interference effects.
A recent expression-focused timing model proposed by
Gallistel and Gibbon (2000), called rate-expectancy theory
(RET), incorporates many of the principles of SET, but
emphasizes rates of outcome occurrence (in the presence and
absence of the cue), rather than latencies between outcomes.
This inversion from waiting times (i.e., latencies) to rates
allows the model to account for stimulus competition-
interference effects because rates of reinforcement associated
with different cues are assumed to summate; in contrast to
SET, RET considers outcome rates attributed to nontarget
discrete cues as well as background cues. Moreover, rein-
forcement rates are assumed to change continuously with ex-
posure to the cue or to the background stimuli in the absence
of as well as with the occurrence of the outcome, thereby ac-
counting for extinction as well as the CS-preexposure effect
and partial reinforcement.
A comparator model that does not focus exclusively on
timing is thecomparator hypothesisof R. R. Miller and
Matzel (1988; also see Denniston, Savastano, & Miller,
2001). In this model, responding is also assumed to be di-
rectly related to the degree to which the target cue predicts the
outcome and inversely related to the degree to which back-
ground (discrete and contextual) cues presentduring training
of the cue predict the outcome. The down-modulating effect
of the background cues on acquired responding depends on
the similarity of the outcome (in all aspects, including tempo-
ral and spatial attributes) that these cues predict relative to the
outcome that the target cue predicts. Thus, this model (along
with contingency theory) brings to acquired responding the
principle of relativity that is seen in many other subfields
concerned with information processing by organisms (e.g.,
Fechner’s law, the marginal value theorem of economics,
contrast effects in motivational theory, the matching law
of behavioral choice as discussed in this chapter’s section
entitled “Instrumental Responding”). The timing expression-
focused models also emphasize relativity (so-called time-
scale invariance), but only in the temporal domain. The
comparator hypothesis accounts for both contingency degra-
dation and cue competition effects through links between the
cue and background stimuli (discrete and contextual) and
links between these background stimuli and the outcome.Conditioned Inhibition. In all of the comparator mod-
els, a conditioned inhibitor is viewed as a stimulus that